In recent years self-adaptive filters have become an important tool in signal processing. For example, when used for echo cancellation, they can often dramatically improve the quality of long distance telephone communications. The basic theory of the self-adapting finite impulse response (AFIR) filter. which simulates or identifies an unknown system has been published by S. J. Campanella et al., "Analysis of an Adaptive Impulse Response Echo Canceller", COMSAT Technical Review, Vol. 2, No. 1, Spring 1972, pp. 1-36; and B. Widrow et al., "Stationary and Nonstationary Learning Characteristic of the LMS Adaptive Filter", Proc. IEEE, Vol. 64, No. 8, August 1976, pp. 1151-1162. The use of AFIR filters for echo cancellation has been described in the papers of Campanella et al, above, and O. A. Horna, "Echo Canceller Utilizing Pseudo-Logarithmic Coding", NTC '77 Conference Record, Vol. 1, pp. 04:7-1-04:7-8; and "Identification Algorithm for Adaptive Filters", COMSAT Technical Review, Vol. 8, No. 2, Fall 1978, pp. 331-351.
The self adaptive filters used for echo cancellation produce optimum echo cancellation if and only if the input signal is a sequence of random samples (i.e., a Poisson wave). Problems arise when the successive input signals are highly correlated as in the case of speech and video signals, for example, and optimum adaptation cannot be achieved.